If a vehicle travels at a constant or uniform speed, the formula that relates distance, speed and time is:

Distance = speed \times time

 

First Case Scenario

The vehicles are travelling towards one another.

{ d }_{ AC }+{ d }_{ CB }={ d }_{ AB }

Two cities, A and B are located 300 miles from each other. At 9 am, a car leaves City A with a speed of 90 mph and travels towards City B. At the same time, a car leaves City B travelling towards City A with a speed of 60 mph. Find:

 

1 The time it takes for the cars to pass each other.

90t+60t=300

150t = 300

t=\frac { 300 }{ 150 }

t=2 hours

 

2 The time at which they passed each other.

They were at 11 of the morning.

 

3 The distance traveled by each at the time of them passing each other.

{ d }_{ AB } = 90 \times 2 = 180 miles

{ d }_{ BC } = 60 \times 2 = 120 miles

 

Second Case Scenario

The vehicles are travelling in the same direction from different starting points.

{ d }_{ AC }-{ d }_{ BC }={ d }_{ AB }

Two cities, A and B are located on the same east-west highway, 180 miles from each other. At 9 am, a car leaves each city, both travelling east. The car that leaves City A travels at 90 mph, and the car that leaves City B travels at 60 mph. Find:

1. The time it takes for Car A to reach Car B:

90t-60t=180

30t=180

t=\frac { 180 }{ 30 }

t=6 hours

2. The time at which Car A reaches Car B:

Car A reaches Car B at 3 in the afternoon.

 

3. The distance traveled by each at the time of Car A reaching Car B:

{ d }_{ AB }=90 \times 6 = 540 miles

{ d }_{ AB }=60 \times 6 = 360 miles

 

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Third Case Scenario

The vehicles are travelling in the same direction with the same starting point.

{ d }_{ 1 } = { d }_{ 2 }

A car leaves a city with a speed of 90 mph. Three hours later and out of the same city another car in pursuit of the first leaves with a speed of 120 mph. Find:

1. The time it takes for the second car to reach the first.

90t = 120 \times (t - 3)

90t = 120t - 360

90t - 120t = -360

-30t = -360

t = \frac { -360 }{ -30 }

t=12 hours

2. The distance from the city when the second car reaches the first.

{ d }_{ 1 } = 90 \times 12 = 1,080 miles

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.